IEICE TRANSACTIONS on Information
Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process
Summary :
This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.
- Publication
- IEICE TRANSACTIONS on Information Vol.E101-D No.7 pp.1843-1859
- Publication Date
- 2018/07/01
- Publicized
- 2018/04/16
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2017EDP7236
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
Authors
Huiming ZHANG
Waseda University
Junzo WATADA
PETRONAS University of Technology
Keyword
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Huiming ZHANG, Junzo WATADA, "Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process" in IEICE TRANSACTIONS on Information,
vol. E101-D, no. 7, pp. 1843-1859, July 2018, doi: 10.1587/transinf.2017EDP7236.
Abstract: This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2017EDP7236/_p
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@ARTICLE{e101-d_7_1843,
author={Huiming ZHANG, Junzo WATADA, },
journal={IEICE TRANSACTIONS on Information},
title={Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process},
year={2018},
volume={E101-D},
number={7},
pages={1843-1859},
abstract={This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.},
keywords={},
doi={10.1587/transinf.2017EDP7236},
ISSN={1745-1361},
month={July},}
Copy
TY - JOUR
TI - Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process
T2 - IEICE TRANSACTIONS on Information
SP - 1843
EP - 1859
AU - Huiming ZHANG
AU - Junzo WATADA
PY - 2018
DO - 10.1587/transinf.2017EDP7236
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E101-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 2018
AB - This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.
ER -
English
